In the field of communication, many communication systems including multiple input multiple output (MIMO) system and orthogonal frequency division multiplexing-code division multiple access (OFDM-CDMA) system are subject to the problem of signal detection. That is, the transmitting signal vector x is detected according to the receiving signal vector y=Hx+n.
Wherein, the channel matrix H and the statistic characteristics (such as Gaussian white noise) of the noise vector n are given, and the elements of the transmitting signal vector x are symbols obtained by way of quadrature amplitude modulation (QAM). In theory, the detecting method which produces minimum error rate is maximum likelihood detection (ML detection), but the complexity increases exponentially along with the dimension of the transmitting signal vector x and the magnitude of modulation, and becomes impractical to actual signal telecommunication system.
To the contrary, despite some detecting methods such as zero forcing method and Lenstra-Lenstra-Lovász (LLL) method have low complexity but the detecting performance is too poor to be accepted in actual systems.
Let the LLL method which is developed from the field of mathematics be taken for example. The contents and object of the LLL method are disclosed below.
Let the channel matrix be expressed as H=└h1, . . . , hnt┘, wherein nt is the number of column vectors, {h1, . . . , hnt} is a set of basis of the lattice. The object of the detecting method is to search for another set of basis {{tilde over (h)}1, . . . , {tilde over (h)}nt} to expand the lattice. It is preferred that the vectors of this new set of basis are shorter and more orthogonal. The spirit and operation of the detecting method lie in the use of Gram-Schmidt orthogonalization process (GSO). The pseudo code of the detecting method is disclosed below:
i=2while (i ≦ nt)hi = hi −┌μi,i−1┘hi−1, update GSOif (||q1 + μi,i−1qi−1||2 < δ||qi−1||2)swap hi−1 and hi, update GSOi=i−lelsefor j=i−2 to 1h1 = h1 −┌μij┘hj, update GSOendi=i+1endend, wherein      GSO    :          [                        h          1                ,                  h          2                ,        …        ,                  h                      n            1                              ]        =                    [                              q            1                    ,                      q            2                    ,          …          ,                      q                          n              1                                      ]            ⁡              [                                            1                                                                                                                                                                                                                                                                                                                                                          μ                                  2                  ,                  1                                                                    1                                                                                                          0                                                                                                                                              μ                                  3                  ,                  1                                                                                    μ                                  3                  ,                  2                                                                    1                                                                                                                                                                                                  ⋮                                      ⋮                                      ⋮                                      ⋱                                                                                                                                              μ                                                      n                    1                                    ,                  1                                                                                    μ                                                      n                    1                                    ,                  2                                                                                    μ                                                      n                    1                                    ,                  3                                                                    …                                      1                                      ]              T  
However, the detecting method still has many technical difficulties:
1. The complexity of the detecting method is related to the basis {h1, . . . , hnt} inputted at the beginning and is nondeterministic. This problem is difficult to handle in terms of hardware operation, and the unpredictable complexity in signal processing makes the design of hardware more difficult.
2. The detecting method aims at outputting another set of basis {{tilde over (h)}1, . . . , {tilde over (h)}nt} which is more orthogonal and can expand the same lattice. Based on the process and result of the detecting method, the properties of the finally outputted result cannot be guaranteed because no parameter is used as a performance index for measuring the orthogonalization of the vector.
Thus, how to develop a signal detecting method which is efficient and can be realized and can improve the performance of error rate in detecting signals when applied to a signal telecommunication system has become an imminent issue to be resolved.